An asymptotic duality between the Oldroyd-Maxwell and grade-two fluid models

Vivette Girault; L. Ridgway Scott. 20 May, 2021.
Communicated by L. Ridgway Scott.


We prove an asymptotic relationship between the grade-two fluid model and a class of models for non-Newtonian fluids suggested by Oldroyd, including the upper-convected and lower-convected Maxwell models. This confirms an earlier observation of Tanner. We provide a new interpretation of the temporal instability of the grade-two fluid model for negative coefficients. Our techniques allow a simple proof of the convergence of the steady grade-two model to the Navier-Stokes model as α → 0 (under suitable conditions) in three dimensions. They also provide a proof of the convergence of the steady Oldroyd models to the Navier-Stokes model as their parameters tend to zero.

Original Document

The original document is available in PDF (uploaded 20 May, 2021 by L. Ridgway Scott).